A basic point that many don’t understand is that a general Adhikāra in Veda for a Class does not arise from a few members of said Class being Brahmavādinīs or being Ṛṣikās.
Secondly, the Ṛṣikā argument is very misleading when you realize that many of the alleged Ṛṣikās are non-human. Where the Ṛṣikā is indeed human, often, the mantras attributed to her are literally quotations or form part of a dialogue that is not in praise of a deity. In contrast, in the overwhelming majority of Ṛṣi sūktas, a deliberate intent to praise the deity or address some supernatural entity can be readily inferred.
In some cases, the Ṛṣikā is a ritual utensil, with the Anukrāmaṇi taking an epithet for the ritual utensil (which happens to be a feminine noun) as the name of the “Ṛṣikā”. This is the state of the Ṛṣikā evidence.
The partially flaky Anukrāmaṇi attributions to Ṛṣis & Ṛṣikās are not a basis for determining Adhikāra. If you take this to its logical conclusion, you will end up with absurdities like one in the next tweet. With this logic, given that some of the most detested enemies of Indra & Bṛhaspati - The Paṇis - are also Ṛṣis for about 5 ṚcaH (5 mantras that is), what should we be inferring? That enemies of the Devas have Adhikāra for learning Veda?
You can’t derive Adhikāra haphazardly on such a flimsy basis. The Adhikāra is expressly & clearly defined in Smṛti & since there is no room to find any contradiction between Smṛti & Śruti, the Smṛti’s rules firmly stand.
This is only a brief overview. A detailed elaboration is required & may be forthcoming.